Fundamentals of Heat and Mass Transfer
7th Edition
ISBN: 9780470917855
Author: Bergman, Theodore L./
Publisher: John Wiley & Sons Inc
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Chapter 4, Problem 4.13P
An electrical heater 100 mm long and 5 mm in diameter is inserted into a hole drilled normal to the surface of a large block of material having a thermal conductivity of
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1 - A square chip, with side w = 5 mm, operates under isothermal conditions.The chip is positioned on a substrate so that its side and bottom surfaces are thermally insulated, while its top surface is exposed to theflow of a refrigerant at T∞ = 15°C.
From reliability considerations, the chip temperature cannot exceed T = 85°C. The refrigerant being air, with a convection heat transfer coefficientcorresponding h = 200 W/(m2K), what is the maximum allowable power for the chip?
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Part a and b
an unsisulated 100 mm diameter steam pipe runs for 25 meters inside a room whose walls and air are at a temperature of 25 C. the superheated steam inside the pipe maintains the temperature at the pipe surface at 150 C. if the natural convection heat transfer coefficient of the air outside the pipe is 10 w/m^2 k and the surface emissivity is 0.8, compute for the convection thermal resistance of the air film surrounding the pipe in k/W
Chapter 4 Solutions
Fundamentals of Heat and Mass Transfer
Ch. 4 - In the method of separation of variables (Section...Ch. 4 - A two-dimensional rectangular plate is subjected...Ch. 4 - Consider the two-dimensional rectangular plate of...Ch. 4 - A two-dimensional rectangular plate is subjected...Ch. 4 - A two-dimensional rectangular plate is subjected...Ch. 4 - Using the thermal resistance relations developed...Ch. 4 - Free convection heat transfer is sometimes...Ch. 4 - Consider Problem 4.5 for the case where the plate...Ch. 4 - Prob. 4.9PCh. 4 - Based on the dimensionless conduction heat rates...
Ch. 4 - Determine the heat transfer rate between two...Ch. 4 - A two-dimensional object is subjected to...Ch. 4 - An electrical heater 100 mm long and 5 mm in...Ch. 4 - Two parallel pipelines spaced 0.5 m apart are...Ch. 4 - A small water droplet of diameter D=100m and...Ch. 4 - A tube of diameter 50 mm having a surface...Ch. 4 - Pressurized steam at 450K flows through a long,...Ch. 4 - The temperature distribution in laser-irradiated...Ch. 4 - Hot water at 85°C flows through a thin-walled...Ch. 4 - A furnace of cubical shape, with external...Ch. 4 - Laser beams are used to thermally process...Ch. 4 - A double-glazed window consists of two sheets of...Ch. 4 - A pipeline, used for the transport of crude oil,...Ch. 4 - A long power transmission cable is buried at a...Ch. 4 - A small device is used to measure the surface...Ch. 4 - A cubical glass melting furnace has exterior...Ch. 4 - An aluminum heat sink (k=240W/mK), used to cool an...Ch. 4 - Hot water is transported from a cogeneration power...Ch. 4 - A long constantan wire of 1-mm diameter is butt...Ch. 4 - A hole of diameter D=0.25m is drilled through the...Ch. 4 - In Chapter 3 we that, whenever fins are attached...Ch. 4 - An igloo is built in the shape of a hemisphere,...Ch. 4 - Prob. 4.34PCh. 4 - An electronic device, in the form of a disk 20 mm...Ch. 4 - The elemental unit of an air heater consists of a...Ch. 4 - Prob. 4.37PCh. 4 - Prob. 4.38PCh. 4 - Prob. 4.39PCh. 4 - Prob. 4.40PCh. 4 - One of the strengths of numerical methods is their...Ch. 4 - Determine expressionsfor...Ch. 4 - Consider heat transfer in a one-dimensional...Ch. 4 - In a two-dimensional cylindrical configuration,...Ch. 4 - Upper and lower surfaces of a bus bar are...Ch. 4 - Derive the nodal finite-difference equations for...Ch. 4 - Consider the nodal point 0 located on the boundary...Ch. 4 - Prob. 4.48PCh. 4 - Prob. 4.49PCh. 4 - Consider the network for a two-dimensional system...Ch. 4 - An ancient myth describes how a wooden ship was...Ch. 4 - Consider the square channel shown in the sketch...Ch. 4 - A long conducting rod of rectangular cross section...Ch. 4 - A flue passing hot exhaust gases has a square...Ch. 4 - Steady-state temperatures (K) at three nodal...Ch. 4 - Functionally graded materials are intentionally...Ch. 4 - Steady-state temperatures at selected nodal points...Ch. 4 - Consider an aluminum heat sink (k=240W/mK), such...Ch. 4 - Conduction within relatively complex geometries...Ch. 4 - Prob. 4.60PCh. 4 - The steady-state temperatures (°C) associated with...Ch. 4 - A steady-state, finite-difference analysis has...Ch. 4 - Prob. 4.63PCh. 4 - Prob. 4.64PCh. 4 - Consider a two-dimensional. straight triangular...Ch. 4 - A common arrangement for heating a large surface...Ch. 4 - A long, solid cylinder of diameter D=25mm is...Ch. 4 - Consider Problem 4.69. An engineer desires to...Ch. 4 - Prob. 4.71PCh. 4 - Prob. 4.72PCh. 4 - Prob. 4.73PCh. 4 - Refer to the two-dimensional rectangular plate of...Ch. 4 - The shape factor for conduction through the edge...Ch. 4 - Prob. 4.77PCh. 4 - A simplified representation for cooling in very...Ch. 4 - Prob. 4.84PCh. 4 - A long trapezoidal bar is subjected to uniform...Ch. 4 - Consider the system of Problem 4.54. The interior...Ch. 4 - A long furnace. constructed from refractory brick...Ch. 4 - A hot pipe is embedded eccentrically as shown in a...Ch. 4 - A hot liquid flows along a V-groove in a solid...Ch. 4 - Prob. 4S.5PCh. 4 - Hollow prismatic bars fabricated from plain carbon...
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- Problem 2 Suppose that heat conduction occurs at a constant rate of đQ/dt in a hollow sphere with an inner radius of r, at temperature T, and an inner radius of r, at temperature T,. Show that for constant thermal conductivity K, the temperature difference between the two surfaces is given by dQ I dT ( 1 т, - т, 1 4л Кarrow_forwardCalculate the quantity of heat conducted per minute through a duralumin circular disc 127 mm diameter and 19 mm thick when the temperature drop across the thickness of the plate is 5 degrees Celsius. Take the coefficient of thermal conductivity of duralumin as 150 W/(m-K).arrow_forwardStainless steel pipes with a thermal conductivity of 17 W/ (m° C) are used to transport hot oil. The temperature inside the tube is 130 ° C. The inner diameter of the pipe is 8 cm and the thickness of the pipe wall is 2 cm. The pipe is then insulated with 4 cm thick insulation with a thermal conductivity of 0.035 W / (m° C). The ambient temperature of the pipe is 25 ° C. Calculate the temperature between the steel and the insulation if we assume a steady state. A picture of the pipe can be seen below.arrow_forward
- A thermometric well is placed in a pipe having diameter of 55 mm. Pipe wall temperature is 100°C and heat transfer coefficient inside the pipe is 300 W/m² K. Thickness of thermowell is 1.2 mm and its length is 50 mm. Thermal conductivity of thermowell material. Is 30 W/mK. If the temperature of the gas flowing through the pipe is recorded by thermometer as 200°C, determine the true temperature of gas. If the error in gas temperature is to be reduced by 80% by increasing the length of thermowell, determine the new length of thermowell. Draw a sketch of this thermowell. Take perimeter to area ratio for thermowell as 1/T (T= thickness).arrow_forward2. A steel plate of k=50w/mk and thickness 10cm passes a heat flux by conduction of 25kW/m² . If the temperature of hot surface of plate is 100C, then what is the temperature of the cooler side of plate?arrow_forwardA spherical shaped vessel of 1.4 m outer diameter is 90 mm thick. Find the rate of heat leakage, if the temperature difference between the inner and outer surfaces is 220°C. Thermal conductivity of the material of the sphere is 0.083 W/mK.arrow_forward
- The temperature distribution across a wall 0.25 m thick at a certain instant of time is T(x) = a + bx + cx², where T is in degrees Celsius and x is in meters, a = 200 C, b = -200 C/m, and c = 30 C/m². The wall has a thermal conductivity of 2.5 W/m.K. (a) Determine the heat flux into and out of the wall (q"in and q'out). (b) If the cold surface is exposed to a fluid at 100 C, what is the convection coefficient h? - Degree Celsius 200°C q" In- q'in q'out= h = Choose... Choose.... Choose... L₂x K = 2.5 W/m.k T(x)-200-200 x +30x² q" Out 142.7 C 11 L=0.25 m Fluid Too = 100 °C harrow_forwardA bare fuel rod has a diameter of 0.373 in and length of 12 ft. The volumetric heat generation rate for this rod is q ′′′ = 10,000 kW/ft3 . The heat produced by the rod is removed by water used as the coolant, at 2250 psia and 575 F. Find the heat transfer coefficient between the bare fuel rod and the coolant. The fuel rod surface temperature is 675 F. [Ans.: h = 2651 Btu/h·ft2 ·F].arrow_forwardAn aluminum tube is 200 cm long and has a outside diameter of 2 cm and wall thickness of 5 mm. One end is kept at a constant temperature of 300°C and the other is kept at a temperature or 10 °C. Assume the tube sides are adiabatic. Calculate the heat transfer through the tube. Use finite difference analysis to calculate the temperature very 10 cms.arrow_forward
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